Skip to main content
SpringerLink
Log in

Restricted Additive Schwarz Method for Nonlinear Complementarity Problem with an M-Function

  • Conference paper
Computer Science for Environmental Engineering and EcoInformatics (CSEEE 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 158))

Abstract

Nonlinear complementarily problem (NCP) is a kind of very important problem. This kind of problem can be arisen from some complicated free boundary problem and other mathematical programming problem. In this paper, numerical solution of NCP with an M-function is considered. A new variant Schwarz method called restricted additive Schwarz method (RAS) is presented. Compared to classical additive Schwarz method, this method has many advantages, such as it reduces communication time while maintaining the most desirable used in practice. Some preliminary numerical results are reported. As we can see from the preliminary numerical results, the restricted additive Schwarz method spends less CPU time and needs fewer iteration numbers then classical additive Schwarz method and PSOR.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bai, Z.Z.: On the Convergence of the Multisplitting Methods for the Linear Complementarity Problem. SIAM J. Matrix Anal. Appl. 21, 67–78 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Frommer, A., Szyld, D.B.: An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms. SIAM J. Numer. Anal. 39, 463–479 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Frommer, A., Szyld, D.B.: Weighted Max Norms, Splittings, and Overlapping Additive Schwarz Iterations. Numer. Math. 83, 259–278 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Xu, H.R., Zeng, J.P., Sun, Z.: Two Level Additive Schwarz Methods for Nonlinear Complementarity Problems with an M Function. Numer. Linear. Algebra Appl. 17, 599–613 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Cai, X.C., Sarkis, M.: A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems. SIAM J. Sci. Comput. 21, 239–247 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cai, X.C., Sarkis, M., Sarkis, M.: A Restricted Additive Schwarz Preconditioner with Harmonic Overlap for Symmetric Positive Definite Linear Systems. SIAM J. Sci. Comp. 41, 1209–1231 (2003)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Jiaying University, Meizhou, Guangdong, 514015, China

    Hongru Xu, Kekun Huang & Shuilian Xie

Authors
  1. Hongru Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kekun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuilian Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dalian University of Technology, Dalian, China

    Yuanxu Yu

  2. Kunming University of Science and Technology, Kunming, China

    Zhengtao Yu

  3. International Association for Scientific and High Technology, Kunming, China

    Jingying Zhao

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xu, H., Huang, K., Xie, S. (2011). Restricted Additive Schwarz Method for Nonlinear Complementarity Problem with an M-Function. In: Yu, Y., Yu, Z., Zhao, J. (eds) Computer Science for Environmental Engineering and EcoInformatics. CSEEE 2011. Communications in Computer and Information Science, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22694-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22694-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22693-9

  • Online ISBN: 978-3-642-22694-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation